Microporous membranes act as selective barriers and play an important role in industrial gas separation and water purification. The permeability of such membranes is inversely proportional to their thickness. Synthetic two-dimensional materials (2DMs), with a thickness of one to a few atoms or monomer units are ideal candidates for developing separation membranes. Here, groundbreaking advances in the design, synthesis, processing, and application of 2DMs for gas and ion separations, as well as water desalination are presented. This report describes the syntheses, structures, and mechanical properties of 2DMs. The established methods for processing 2DMs into selective permeation membranes are also discussed and the separation mechanism and their performances addressed. Current challenges and emerging research directions, which need to be addressed for developing next-generation separation membranes, are summarized.